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C32×C11×Dic11⋊C5 #36344970

order21780
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C11 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×Dic11⋊C5
unambiguous semidirect productDic11⋊(C32×C5×C11)
unambiguous semidirect product(C11⋊C5)⋊(C32×C4×C11)
unambiguous semidirect product(C3×Dic11)⋊(C3×C5×C11)
unambiguous semidirect product(C32×Dic11)⋊(C5×C11)

Splittings

derivedC11 ⋊ C32×C4×C5×C11
HallC32×C11×C11⋊C5 ⋊ C4
HallC32×C11×Dic11 ⋊ C5
HallC32×C112 ⋊ C4×C5
HallC11×C11⋊C5 ⋊ C32×C4
HallC11×Dic11 ⋊ C32×C5
SylowC112 ⋊ C32×C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11AGL(1,𝔽11)
commutator, hypocenterC11C32×C4×C5×C11
FrattiniC2C32×C11×AGL(1,𝔽11)
Fitting, socleC2×C32×C112C2×C5
prime radicalC2×C32×C11×C11⋊C5C2
cosocleC2×C11C2×C32×C5×C11
LCSG ▷ C11
UCSC1 ◁ C2×C32×C11

156 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 319);